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Abstract
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Let A,ℬ denote two families of
functions a,b : X → Y. A function F : Z ⊆ Y → Y is said to operate in (A,ℬ)
provided that for each a ∈ A with range (a) ⊆ Z we have F(a) ∈ℬ. Let G denote a
locally compact Abelian group. In this paper we characterize the functions which
operate in two cases:
- A = Φr(G) = positive definite functions on G with ϕ(e) = r and
ℬ = Oi.d.,s(G) = infinitely divisible positive definite functions on G with
ϕ(e) = s.
- A = ℬ = Φ1(G) = Log Φi.d.,1(G).
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Mathematical Subject Classification
Primary: 42.54
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Milestones
Received: 12 July 1966
Published: 1 February 1968
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